bandpass butterworth filter implementation in C++

Question

I am implementing an image analysis algorithm using openCV and c++, but I found out openCV doesnt have any function for Butterworth Bandpass filter officially. in my project I

Answer 1

I finally found it. I just need to implement the following code from matlab source code to c++ . "the_mandrill" were right, I need to add the normalizing constant into the coefficient:

kern = exp(-j*w*(0:length(b)-1));
b = real(b*(kern*den(:))/(kern*b(:)));

EDIT: and here is the final edition, which the whole code will return numbers exactly equal to MATLAB :

double *ComputeNumCoeffs(int FilterOrder,double Lcutoff, double Ucutoff, double *DenC)
{
    double *TCoeffs;
    double *NumCoeffs;
    std::complex *NormalizedKernel;
    double Numbers[11]={0,1,2,3,4,5,6,7,8,9,10};
    int i;

    NumCoeffs = (double *)calloc( 2*FilterOrder+1, sizeof(double) );
    if( NumCoeffs == NULL ) return( NULL );

    NormalizedKernel = (std::complex *)calloc( 2*FilterOrder+1, sizeof(std::complex) );
    if( NormalizedKernel == NULL ) return( NULL );

    TCoeffs = ComputeHP(FilterOrder);
    if( TCoeffs == NULL ) return( NULL );

    for( i = 0; i < FilterOrder; ++i)
    {
        NumCoeffs[2*i] = TCoeffs[i];
        NumCoeffs[2*i+1] = 0.0;
    }
    NumCoeffs[2*FilterOrder] = TCoeffs[FilterOrder];
    double cp[2];
    double Bw, Wn;
    cp[0] = 2*2.0*tan(PI * Lcutoff/ 2.0);
    cp[1] = 2*2.0*tan(PI * Ucutoff / 2.0);

    Bw = cp[1] - cp[0];
    //center frequency
    Wn = sqrt(cp[0]*cp[1]);
    Wn = 2*atan2(Wn,4);
    double kern;
    const std::complex result = std::complex(-1,0);

    for(int k = 0; k<11; k++)
    {
        NormalizedKernel[k] = std::exp(-sqrt(result)*Wn*Numbers[k]);
    }
    double b=0;
    double den=0;
    for(int d = 0; d<11; d++)
    {
        b+=real(NormalizedKernel[d]*NumCoeffs[d]);
        den+=real(NormalizedKernel[d]*DenC[d]);
    }
    for(int c = 0; c<11; c++)
    {
        NumCoeffs[c]=(NumCoeffs[c]*den)/b;
    }

    free(TCoeffs);
    return NumCoeffs;
}